Wildcat Coffee Inc., uses four types of coffee beans (Columbia, Java, Brazil, an

Question

Wildcat Coffee Inc., uses four types of coffee beans (Columbia, Java, Brazil, and South Africa) as mixtures to manufacture its three coffee products (Everyday, Energy, and Excellence). The cost per pound, the availability, and rating information of the coffee beans are as follows.

Coffee product tests are used to provide ratings on a scale of 0-100, with higher ratings indicating higher product performance. Here are the three coffee products and their product information:

Due to the popular demand of the gourmet segment, at least 920 pounds of Excellence must be produced.

Set up a linear programming model for the above problem.

Coffe Bean Cost Per Pound Caffeine Rating Taste Ratting Aroma Rating Availabie Pounds Columbia 2.10 68 89 90 700 Java 1.50 79 65 77 850 Brazil 1.75 81 78 95 1000 South Africa 1.15 58 68 59 1200

Explanation / Answer

SOLUTION:

Decision variable :As shown in fig1.How much to use each of coffee bean to produce the coffee product.

Let DC indicate the pounds of Columbia beans used to produce a pound of Everyday coffee and

DJ indicate the pounds of Java beans used to produce a pound of Everyday coffee

DB indicate the pounds of Brazil beans used to produce a pound of Everyday coffee

DS indicate the pounds of South Africa beans used to produce a pound of Everyday coffee

NC indicate the pounds of Columbia beans used to produce a pound of Energy coffee

NJ indicate the pounds of Java beans used to produce a pound of Energy coffee

NB indicate the pounds of Brazil beans used to produce a pound of Energy coffee

NS indicate the pounds of South Africa beans used to produce a pound of Energy coffee

XC indicate the pounds of Columbia beans used to produce a pound of Excellence coffee

XJ indicate the pounds of Java beans used to produce a pound of Excellence coffee

XB indicate the pounds of Brazil beans used to produce a pound of Excellence coffee

XS indicate the pounds of South Africa beans used to produce a pound of Excellence coffee

Objective: Max 2.2*(DC+DJ+DB+DS)+2.8*(NC+NJ+NB+NS)+3.5*(XC+XJ+XB+XS) - 2.1*(DC+NC+XC) - 1.5*(DJ+NJ+XJ) - 1.75*(DB+NB+XB) - 1.15*(DS+NS+XS)

s.t.

DC+DJ+DB+DS = 1

NC+NJ+NB+NS = 1

XC+XJ+XB+XS = 1

68DC+79DJ+81DB+58DS >= 65(DC+DJ+DB+DS)

68DC+79DJ+81DB+58DS <= 72(DC+DJ+DB+DS)

89DC+65DJ+78DB+68DS >= 74(DC+DJ+DB+DS)

68NC+79NJ+81NB+58NS >= 77(NC+NJ+NB+NS)

89NC+65NJ+78NB+68NS >= 70(NC+NJ+NB+NS)

89NC+65NJ+78NB+68NS <= 80(NC+NJ+NB+NS)

90NC+77NJ+95NB+59NS >= 80(NC+NJ+NB+NS)

89XC+65XJ+78XB+68XS >= 81(XC+XJ+XB+XS)

90XC+77XJ+95XB+59XS >= 88(XC+XJ+XB+XS)

This constraint is not used in LP formulation - "Due to the popular demand of the gourmet segment, at least 920 pounds of Excellence must be produced", because availability of coffee beans is not given in the question. Therefore, decision variables are not in terms of quantity, but proportion of each coffee beans to blend to make each coffee type.

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